Gomez said:
Just a little note on the 1920's. There is a little thing called
prohabition!

While William T. Llewellyn-Phelps would normally have a glass of wine with his dinner. He would only do it at his home or at a speakeasy.
Whoops! I have failed myself... how stupid of me to totally forget about that VERY important part of the 1920s... whoops...

Well, it was, uh, umm, grape juice. Yeah, that's it.
As to the pacing/speed of the game, I don't think as much you're doing anything wrong as that there's not really a lot going on... not a diss or anything, it's just the "Prologue" to a big campaign, so things will be slow. I might not be the right one to give advice, but I'm running a "Cthulhu feel" horror campaign (the Resurrection City threads), and I use Chaosium scenarios - more or less.
Point is, don't be afraid to abridge certain portions. Or, if all else fails and we don't pick up on a vital lead or clue, don't be afraid to have an NPC drop by to give us a nudge.
Another point: sometimes it may seem rude (I'm not sure what the accepted 'timeframe' is on this), but this may be it, since I believe you said you're new to PbP. Don't be afraid to take over running a character or dictating his actions if the player's not around. Rather than waiting on that person's post, just dictate what someone does. Especially in combat. Being COC, we shouldn't have a lot of that, but it's a thought.
Sometimes you just have to take things in your own hands, you know? Now, of course, don't abuse this, though.
Like I said, not sure on the accepted period you should wait before NPCing a character, maybe some others on here know. I know I usually do it if I'm ready to make a post. And then when I do NPC someone, I'll have them do something minor. Maybe ask someone a question, or give them an item, or something.
Just some hints I've learned from my PbP experience (DMing 3 games currently, playing 2-3, counting this one).